Pattern can be identified in many forms. Mathematicians appreciate pattern and its ability to describe, to explain, to determine, to create a sense of security--"I can see a pattern...", and pattern is part of the sense making process for learners, from a very early age. Number squares exhibit a multiplicity of patterns that may vary according to…

As with much in life the term "investigative", when used to describe an approach to teaching and learning, can have many interpretations. Some might consider that the term "investigations" is somehow "mired in the past", others might consider "investigations" to be a "credo" that sustains their own mathematics teaching and learning. With…

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

We are frequently told that Hong Kong has a model system for learning mathematics. In this article Daniela Vasile notes one short-coming in that the pupils are not taught to problem-solve. She begins with a new class by asking them to write down the craziest equation they can come up with and bases her whole lesson, and the following homework,…

Of the four mathematical operators, division seems to not sit easily for many learners. Division is often described as "the odd one out". Pupils develop coping strategies that enable them to "get away with it". So, problems, misunderstandings, and misconceptions go unresolved perhaps for a lifetime. Why is this? Is it a case of "out of sight out…

To most children in primary school role-play is just something you do, and something you enjoy. It is part-and-parcel of being at school, part of the normal classroom activity. So, why can it not just be a normal part of learning mathematics? Can we study learners "in role", and make judgments about what they learn, and how they learn? This is the…

The notion of "understanding", and its place in the learning process, is often placed in sharper focus when considered in the context of learning and teaching algebra. There are tensions between "doing" algebra, following algorithms, using "rules", or "tricks", and understanding "what you are doing". How does this impact the "way" that algebra is…

Games are for playing, more often than not playing a game is a social experience, it is fun, and we all enjoy playing games. Play and playing are ways in which we learn, so how often are games part of the normal activity of the mathematics classroom? The answer, in most cases, has to be--not often. Is it that games just don't seem to fulfil the…

When it comes to using software to enhance the learning and teaching of mathematics it is all too easy to "talk the talk", but "walking the walk" is something else. There are many pertinent problems associated with accessibility, robust systems, curriculum time, classroom management, software familiarity and intuitive usage to name but a few.…

Symbolism is an important element within mathematical notation. Symbolism enables unambiguous communication of mathematical ideas and forms. Current mathematical symbolism is the result of much evolution and acceptance by those working in the field. When is it appropriate to challenge accepted norms and suggest alternatives or "changes"?…

What is it that makes learners "think"? What geometrical problem, simply posed, can switch on the thinking processes of students? The author describes one such starting point that worked in a real classroom with Year 9 students. A group of learners for whom "mathematics comes easy" experience being stuck, they learn to handle this unfamiliar…

Islamic patterns were a regular feature in mathematics classrooms, and probably still feature in many wall displays. However, as part of the learning process, these ancient designs appear to have lost any significant contemporary appeal. Here, the power of software is engaged to bring the construction of Islamic type patterns up to date. Forget…

This is the opportunity to be an "insider" into the process of one person's experience of working on a mathematical problem. The experience is enhanced through the support and intervention of a learning mentor who "knows" the learner. This mentor/learner dialogue is documented to describe the problem solving journey. It shows…

The potential, for the learner, of a maths trail was documented in MT219. Here, the focus is on the planning element of such an event from the perspective of a group of student teachers. Personal reactions, and insights are used to demonstrate that "real, and authentic, learning" takes place for all those involved in the activity.

Many learners still struggled to appreciate, and understand the difference between, the concepts of fractions and ratio. This is not just a UK phenomenon, which is demonstrated here by the use of a resource developed by the Wisconsin Centre for Education, in association with the Freudenthal Institute of the University of Utrecht, with a group of…